Data is in object type instead of int, have to get rid of comma after thousands

On first glance there seems to be yearly seasonality in the data
Not the best result, residuals are huge

Resampling to remove the weekly seasonality

Looks better now, clear yearly seasonality

Checking for another seasonality

Time series appears to contain weekly seasonal component as well
No idea how to take both into account, going to stick with resampled weekly data

Checking stationarity

p-value is below 0.05, time series is stationary

Checking correlations

Based on the plots, might be AR(3) model

Starting out with auto-arima

Train-test split

Simple Exponential Smoothing

Holt's method

Just exponential gives the smallest error

Holt-Winter's method

Additive trend and multiplicative seasonal component gives lowest MAPE

SARIMA

Prophet

Going back to normal dataframe

Plotting all of the best models

Based on these results, Holt's method that looks just at the current trend is the best. This might be caused by ignoring the seasonal component or the fact that time series for this month keeps going down instead of staying at a level like for the past 5 years. Both of these facts shouldn't matter for the final forecast since we expect the time series to go up. Another possibility is that our residuals don't resemble white noise.

Final forecast for 4 weeks into the future

We can see that SARIMA, Prophet and Holt-Winter's all follow the yearly trend and go upwards in september, with the main difference between them being their starting value and how fast they increase. SES stays level with the last data point, while Holt's method follows the last observed trend and keeps decreasing. We can safely assume that if the pattern observed in the last 5 years stays the same both of these methods will give really bad forecasts.

Testing out differencing to remove the yearly seasonal compontent.

Checking stationarity

p-value is below 0.05, time series is stationary

Checking correlations

We have a lot of correlations.

Starting out with auto-arima

Train-test split

Simple Exponential Smoothing

Holt's method

Errores for both SES and Holt are too big to even consider them for final forecast.

Holt-Winter's method

Still really big MAPE.

SARIMA

Prophet

Going back to normal dataframe

Plotting all of the best models

Even though the MAPE were really big, the forecasts don't look too bad. Have to invert differencing to really make sure but will leave that for after final forecast.

Final forecast for 30 days into the future

Inverting differencing

Because of the weekly differences it's hard to notice changes but we can see that there is a clear upwards trend. The downside is that the differences between days might be too big compared to the previously analysed models. Looking at forecasts, Prophet seems to be doing the best with the smallest overall changes between highs and lows while still keeping up with expected increase in traffic.

Testing out Prophet with both yearly and weekly seasonality

Comparing all of the obtained results with final Prophet model as baseline for best fit.

Using original time series for forecasts with weekly seasonality

Starting out with auto-arima

Train-test split

Simple Exponential Smoothing

Holt's method

Errores for both SES and Holt are too big to even consider them for final forecast.

Holt-Winter's method

Still really big MAPE.

SARIMA

Prophet

Going back to normal dataframe

Plotting all of the best models

Holt-Winter's method is once again the best. Sarima undervalues points every time, while prophet goes too far in both directions.

Final forecast for 30 days into the future

Even though Holt-Winter's method had the lowest MAPE it doesnt matter for the final forecast, since it doesn't take into account the yearly trend. Same thing happens with SARIMA. At this point i'm almost certain that no matter what I type into prophet it automatically searches for seasonal trends, taking them both into account - there seems to be no other explanation why it can go up otherwise, giving it the best forecast across all models i investigated today.